Question

X and Y are points of linear on the sides AB and AC respectively of a triangle ABC such that $\frac{AX}{AB}=\frac{1}{4}$, AY = 2 cm and YC = 6 cm. Find whether $XY||BC$ or not

Answer 1

$\frac{AX}{AB}=\frac{1}{4}$

i.e., $AX=1m,AB=4m$ (m - constant)

$\therefore BX=AB-AX$

$=4m-1m=3m$

Now, $\frac{AX}{XB}=\frac{1K}{3K}=\frac{1}{3}$

And, $\frac{AY}{YC}=\frac{2}{6}=\frac{1}{3}$

$\frac{AX}{XB}=\frac{AY}{YC}$

$\therefore XY||BC$ (By converse of Thales' theorem)